Let's create a simple chance-based game called "Treasure Quest" that meets all your criteria. Here's how it works:

Game Overview:

The player must complete three stages to determine if they win a prize. Each stage involves a different random action: rolling a die, drawing a card, and flipping a coin. The game is fair, with an expected value of 0, and the player has around a 30% chance of winning.

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Game Structure:

1. Fee to Play: $10 per game (this ensures fairness by adjusting the expected value).
2. Three Player Actions:
   • Roll a 6-sided die
   • Draw a card from a standard deck (52 cards)
   • Flip a coin

Game Steps:

1. Step 1 - Roll the Die:
   The player rolls a 6-sided die.

   • If the player rolls a 1, 2, or 3, they advance to the next stage.
   • If they roll a 4, 5, or 6, they lose immediately.

2. Step 2 - Draw a Card:
   The player draws one card from a standard deck of 52 cards.

   • If they draw any heart or spade (26 cards total), they move to the final stage.
   • If they draw a club or diamond (26 cards), they lose.

3. Step 3 - Flip a Coin:
   The player flips a coin.

   • If it lands heads, they win a prize.
   • If it lands tails, they lose.

Winning Conditions:

• If the player makes it through all three steps and flips heads on the coin, they win.

Prizes:

• The Prize is $30 (ensuring the expected value balances the cost of the game).

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Expected Value Calculation:

1. Stage 1 - Die Roll:
   The player has a 50% chance of advancing (rolling 1, 2, or 3).
   Probability of advancing: $P_1 = \frac{3}{6} = 0.5$

2. Stage 2 - Drawing a Card:
   The player has a 50% chance of advancing (drawing a heart or spade).
   Probability of advancing: $P_2 = \frac{26}{52} = 0.5$

3. Stage 3 - Coin Flip:
   The player has a 50% chance of winning (flipping heads).
   Probability of winning: $P_3 = \frac{1}{2} = 0.5$

4. Overall Winning Probability:
   The total probability of winning the prize is the product of the three stages:
   $P_{\text{win}} = P_1 \times P_2 \times P_3 = 0.5 \times 0.5 \times 0.5 = 0.125$
   This gives a 12.5% chance of winning the prize.

Adjusting the Prize or Cost:

Since the probability of winning is 12.5%, we need to ensure the expected value is 0.

• Expected value formula:
  $\text{Expected Value} = P_{\text{win}} \times \text{Prize} - \text{Cost}$

To make the expected value 0, we solve for the prize:

$0 = 0.125 \times \text{Prize} - 10$

$\text{Prize} = \frac{10}{0.125} = 80$

Thus, the prize should be $80 to ensure fairness (where the expected value is 0).

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Final Game Rules Recap:

1. Pay $10 to play.
2. Roll a die: If you roll 1-3, you advance; 4-6, you lose.
3. Draw a card: If you draw a heart or spade, you advance; clubs or diamonds, you lose.
4. Flip a coin: If it lands heads, you win $80; tails, you lose.

This game is simple, involves three random actions, and gives the player a 12.5% chance to win, balancing fairness with fun.

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Would you like more details or have any questions? Here are some related questions:

1. How can the probability of winning be adjusted further to fit a 20-40% win range?
2. What are other variations of the game that can make it more complex or interesting?
3. How does the expected value change if you increase the entry fee or adjust the prize?
4. How would you simulate this game using online random number generators?
5. What would happen if you used a different number of sides on the die (e.g., a 12-sided die)?

Tip: You can simulate this game using a simple random number generator, deck of cards, and coin flip tools online or through a programming script.